A to Z Exams

If the roots of the equation 4x3-12x2+11 x + k = 0 are in arithmetic progression, then k is equal to :

If f(x) is a polynomial of degree n with rational coefficients and 1+2i, 2-√3 and 5 are three roots of       f(x) = 0, then the least value of n is :

If cos 2x = (√2 + 1)(cos x - 1/√2) , cos x ≠ 1/2 then x belongs to

The sum of the fourth powers of the roots of the equation x5+px3+qx2+s=0 is

If the roots of x4+5x3-30x2-40x+64=0 are in G.P then the roots are

If A,B,C are the remainders of x3-3x2-x+5,3x4-x3+2x2-2x-4,2x5-3x4+5x3-7x2+3x-4 when divided by x+1,x+2,x-2 respectively then the ascending order of A,B,C is

If α and β are different values of x satisfying a cos x+b sin x=c then tan (α+β/2) =

If x2+p1x+q1=0,x2+p2x+q2=0,x2+p3x+q3=0 has a common root,then p12+p22+p32+4(q1+q2+q3)=

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

The roots of x3-3x2+4=0,when there is a multiple root,are

The equations whose roots are exceed by 2 than those of x4+x3-10x2+4x+24=0 is

If 2,-2,4 are the roots of ax3+bx2+cx+d=0 then the roots of 8ax3+4bx2+2cx+d=0 are

If α+β+γ=1,α2+β2+γ2=2 and α3+β3+γ3=3,then α5+β5+γ5=

If the equations x2-x-p=0 and x2+2px-12=0 have a common root,then that root is

If a=cos 2π/7+i sin 2π/7,α=a+a2+a4 and β=a3+a5+a6 then α,β are the roots of the equation

The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are

The roots of x4-5x3+3x2+19x-30=0 are

If α,β are the roots of 8x2-3x+27=0 then the value of (α2/β)1/3+(β2/α)1/3 is

The roots of x3+x2-2x-2=0 are

The transformed equation of x3-4x2+1/4x-1/9=0,by eliminating fractional coefficients is

The remainder when 2x5-3x4+5x3-3 x2+7x-9 with x2-x-3 is

The equations whose roots are diminish by 3 than those of x4-5x3-20x2+3x+17=0 is

If α,β,γ are the roots of x3+x2+x+1=0 then α3+β3+γ3=

If one root of the equation ix2-2(1+i)x+(2-i)=0 is 2-I,then the other root is

Match the following. Equation Roots I.x3-3x2-16x+48 =0 a)6,4,-1 II.x3-7x2+14x-8=0 b)1,1/3,1/5 III.15x3-23x2-9x-1=0 c)1,2,4 IV. x3-9x2+14x+24=0 d)4,-4,3

If α,β,γ are the roots of x3+3px+q=0 then the equation whose roots are α+1/β+γ–α,β+1/γ+α–β and γ+1/α+β–γ is

If the quadratic equations ax2+2cx+b=0 and ax2+2bx+c=0 (b≠c) have a common root,then a+4b+4c=

If α,β,γ are the roots of x3+2x2-3x-1=0,then the value of α-4+β-4+γ-4 is

If A12/x-a1+A22/x-a2+.... Ak2/x-a k=m and ai,AI,m are rational then the equation has

If the sum of two of the roots of 4x3+16x2-9x-36=0 is zero then the roots are